Hence, the proof is completed by choosing the identities of the rules.
Trigonometry identities
Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle. The trigonometric identities hold true only for the right-angle triangle.Given that :
Complete the proof of the identity by choosing the Rule that justifies each step.
Sin^2x + 4cos^2x = 4 -3sin^2x
Statement Rule
[tex]sin^{2} x + 4 cos^{2}x[/tex]
= [tex]sin^{2}x + 4 (1 - sin^{2} x )[/tex] [tex]sin^{2}u + cos^{2}u = 1[/tex]
[by using Pythagorean identities]
= [tex]sin^{2}x + 4 - 4 sin^{2}x[/tex] [tex](1 - sin^{2}x )[/tex]
[ multiplied by 4 ]
= [tex]4 - 3 sin^{2}x[/tex]
Sin^2x + 4cos^2x = 4 -3sin^2x
Hence proved.
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Kyra is blocking off several rooms in a hotel for guests coming to her wedding. The hotel can reserve large rooms that can hold 4 people, and small rooms that can hold 3 people. Kyra reserved twice as many large rooms as small rooms, which altogether can accommodate 77 guests. Determine the number of small rooms reserved and the number of large rooms reserved.
Answer:
19 small room and 25 big room
Step-by-step explanation:
nonlinear solver methods can find different final values that depend on the starting values of your decision variables.
Nonlinear solver method used in the slope of the objective function as the input values changes. It determines that it reached at the optimum solution when the initial value is equals to zero.
In the nonlinear solver method, the initial values used within one of the nonlinear equation. By default the initial value chosen for all variables is zero or the lower bound. zero is in many cases is a bad initial value for a nonlinear variable. For example, if the variable appears in a product term since the initial derivative becomes zero, and it appears as if the function does not depend on the variable. When the equation is simple, the value of x can be determined analytically. This is used in the case when x can be written explicitly by applying mathematical operations or when a known formula such as the formula for solving a quadratic equation can be used to determine the exact value of x.
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3x+5y = 4
Constant?
Change?
4x2 + y = 4
Constant?
Change?
6x + 1 = y
Constant?
Change?
Answer:
Step-by-step explanation:
missing angle of 28 and 21 with trigonometry
Answer:
Step-by-step explanation:
as suggested, use SOH CAH TOA
we are given the H and O and want an angle
use SOH, b/c it's got the two given pieces of info
Sin(∅) = Opp / Hyp
Sin(x) = 21 / 28
arcSin ( Sin(x)) = arcSin(21/28)
x = 48.59°
what are the first six terms for a₁ = -9, d=8?
a₁ = -9
a₂ = -9 + (2 - 1) * 8 = -9 + 8 = -1
a₃ = -9 + (3 - 1) * 8 = -9 + 16 = 7
a₄ = -9 + (4 - 1) * 8 = -9 + 24 = 15
a₅ = -9 + (5 - 1) * 8 = -9 + 32 = 23
a₆ = -9 + (6 - 1) * 8 = -9 + 40 = 31
standard form of (2 ten thousands 7 thousands) divided by 10
Answer:
2,700
Step-by-step explanation:
10,000x2=20,000+7,000=27,000÷10=2,700
What is the slope of the line that passes through the points (-1, 2) and (-4, 3)? i need this now
-3
3
1/3
-1/3
Answer:
m = -1/3
Step-by-step explanation:
(-1, 2) and (-4, 3)
m = 3-2/-4+1
m = 1/-3
m = -1/3
Steve is m years old. His brother, Jack, is n years older than Steve. How old will Jack be in 2 years?
Answer:
n+m+2 years
Step-by-step explanation:
m=Steve's age.
J=Jack's age.
n=Age difference between Steve and Jack
J=n+m
J+2=n+m+2 years
finding missing angle of 32 and 17 with trigonometry
An organization needs to reach out to a specific target audience, and has decided that it wants to use social media advertising to do so. It wants to buy specific keywords to accurately target the audience who would want to see these ads. The aim is to get a high effective exposure rate and engagement rate without invading consumer privacy. Which of the following advertising revenue models would best suit the organizations' needs? a. Bidding for ad words b. Pay-per-click c. I-Traffic Index d. Pop-under ads e. Bidding for ad space
The advertising revenue models would best suit the organization needs is option (A) Bidding for ad words
Here the organization wants to buy specific keywords to accurately target the audience who would want to see these ads
The aim of the organization is to get a high effective exposure rate and engagement rate without invading consumer privacy
Bidding for ad words states that the amount of money you are willing to spend for a single click on a given keyword.
Here they will get high effective exposure rate and engagement rate without invading consumer privacy
Therefore, the best advertising revenue model is option (A) Bidding for ad words
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Please help with attached linear function question. Thank you!!
The graph of cubic equations, a to d and the associated cubic equations are as follows;
Equation (B) ⇒ Graph a
Equation (C) ⇒ Graph b
Equation (D) ⇒ Graph c
Equation (A) ⇒ Graph d
What is a cubic equation?A cubic equation that has only one variable is an equation of the form a·x³ + b·x² + c·x + d, where a ≠ 0.
The evaluation of the graphs are as follows;
Graph a
The y-intercept of the graph a, is 1, and the x-intercept, which is a solution of the equation is x = -1,
Therefore, when x = 0, y = 1, and when y = 0, x = -1
The function in graph a represents the translation of the parent function, y = x³, one unit, upwards, which corresponds with the function;
y = x³ + 1
Therefore, graph a corresponds to cubic equation (B) y = x³ + 1
Graph b
The y-intercept is one (1), and the turning point is at the point x = -1, which represents a shift of one unit to the left, and which can be obtained by the equation; y = (x + 1)³
Therefore, graph b corresponds with the cubic equation (C) y = (x + 1)³
Graph c
The turning point of the graph and the y-intercept is shifted one unit down, which corresponds with the equation; (D) y = x³ - 1
Graph d
The turning point is shifted 1 unit to the right and is located on the x-axis, The y-intercept is located at the point y = 1, therefore, the graph corresponds with the equation y = (x - 1)³
Graph d corresponds to equation (A), y = (x - 1)³
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Find the derivative of f(x) = 3x² + 2x at 3. That is, find f '(3).
Answer:
20
Step-by-step explanation:
To find the derivative of f(x) = 3x² + 2x at x = 3, we can use the power rule:
f'(x) = 2*3x + 2
When x = 3, the derivative of f(x) is:
f'(3) = 2*3(3) + 2
f'(3) = 18 + 2
f'(3) = 20
Therefore, the derivative of f(x) = 3x² + 2x at x = 3 is f'(3) = 20.
Carli is comparing two phone companies. Big Phone Company charges $0.39 for the connection fee and $0.03 per minute. Little Phone Company charges $0.25 for the connection fee and $0.07 per minute. Which system of equations could be used to determine the total cost, y, for using x minutes?
Answer:
Step-by-step explanation:
I also need help.
The base of a solid is bounded by the graphs of the given equations. The cross section of the solid taken perpendicular to the y- axis is a square. Write, butt do not evaluate, an integral expression that gives the volume of the solid where
y=x,y=2,x=6
An integral expression that provides the solid's volume at the points y=x, y=2, and x=6 is [tex]\int\limits^{6}_{2} {y^3} \, dy[/tex]
How many areas of space are filled by an object is determined by its volume. The amount of unit cubes required to completely fill the solid serves as the measurement. By counting the solid's unit cubes, the answer can be determined.
A three-dimensional object's volume is typically thought of as its ability to accommodate matter.
According to the question,
The cross section of the solid taken perpendicular to the y- axis is a square.
Solid base equation: y=x, y=2, x=6
Square Volume = (Side3)
Since y = x in the equation and y = 2 as a result, x must equal 2.
So , Limit of x varies from 2 to 6
Volume of solid is [tex]\int\limits^{6}_{2} {y^3} \, dy[/tex]
Hence , , an integral expression that gives the volume of the solid is [tex]\int\limits^{6}_{2} {y^3} \, dy[/tex]
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Corresponding angles formed by two parallel lines intersected by a transversal are always:
complementary.
congruent.
acute.
obtuse.
supplementary
Answer:
Congruent
Step-by-step explanation:
If you slide the angle down the transversal, it would land perfectly on top of the corresponding angel and you would be able to see that they are congruent.
Question 6 A test of hypothesis was performed to determine, at 5% level of significance, if the majority of the engineering graduates pass the PE exam in their first try. If the computed value of the test statistic Z based on the sample information is z = 2.10, then the p-value for this test is: 0.00895 O 0.05 0.9821 None of these O 0.0179 N • Previous Not saved S
The p-value for the test is 0.9821.
What is hypothesis?
A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters through hypothesis testing.
What is z-score?
You can plot a z-score on a normal distribution curve. The range of Z-scores ranges from -3 standard deviations (which would be on the far left of the normal distribution curve) to +3 standard deviations (which would fall to the far right of the normal distribution curve). You must be aware of the mean and population standard deviation in order to use a z-score.
Given that the test statistic Z based on the sample information is z = 2.10.
z = 2.1 + 0.00
From the z-score table the value of p is 0.9821.
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Question 7
The cone would fit into the beachball two times, and has a volume of 134 in^3. Answers required are:
Blank 1 - two
Blank 2 - 134 in^3.
A beachball has the shape of a sphere, so that its volume can be determined by;
volume of a sphere = 4/3 [tex]\pi r^{3}[/tex]
where r is the radius of the sphere.
Given that the diameter of the beachball is 8 inches, then;
its radius = 8/ 2
= 4 inches
volume of beachball = 4/3 x 22/7 x 4^3
= 268.19 cubic in.
The volume of a cone can be determined by;
volume of a cone = 1/3 [tex]\pi r^{2} h[/tex]
where r is its radius, and h is its height.
Given a cone of radius 4 inches and height 8 inches, then;
its volume = 1/3 x 22/7 x 4^2 x 8
= 134.1cubic inches
Thus,
268.19/ 134.10 = 1.999993
≅ 2.0
Thus the cone would fit into the beachball twice, and its volume is 134.10 in^3.
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as the class finishes what do you see as the most useful tools or knowledge you will be able to use in the professional world? part two: elaborate on the business research project and what you learned about your topic and about the research process. compose two fully-developed paragraphs that address each area to the fullest.
The business research project was a valuable experience that taught me about the importance of research in the business world and the various methods and techniques that can be used to conduct effective research.
One of the most useful tools or knowledge that I will be able to use in the professional world after completing this class is the ability to analyze and interpret data. This includes the ability to perform statistical analysis and draw meaningful conclusions from data sets. This skill is crucial in today's business world, as data-driven decision-making is becoming increasingly important in all industries.
In the business research project, I learned about the importance of conducting thorough research in order to make informed decisions. I also learned about the various methods of conducting research, such as primary and secondary research, and the pros and cons of each method. I also learned about the importance of using reliable sources and properly citing sources in order to ensure the credibility of my research.
It also helped me to develop my analytical skills and the ability to interpret data in order to draw meaningful conclusions. These skills will be essential in my future professional career as I work to make informed decisions and solve complex business problems.
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Prove Statement 5.38: Let T be the relation on Z defined by (m,n) ∈T iff m−n is divisible by 3 . Prove T is an equivalence relation.
If n is devisible by 3 then n^2 is devisible by 3 it easy.
n=3k so n^2=9k so 9 is devisible by 3.
In the other way, if n^2 is devisible by 3we have n^2=3k wher k is integer number which has to be devisible by 3. If k is not devisible by 3, then n=/sqrt3*r , r^2=k. So n is not integer, contradiction.
This proof show us that iff doesnt work.
If n is devisile by 4 then n^2 is also devisible by 4. But if we have that n^2 is devisibke by 4 then n hasn’t be devisible by 4. Example: n^2=36 is dev by 4 but n=6 is not dev by4.
Its allow because /sqrt 4 is 2.
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Which figure has four sides that are the same length
TRUE/FLASE. It's easier to come up with the correctness proof of the divide and conquer algorithm compared to the greedy algorithm.
It's easier to come up with the correctness proof of the divide and conquer algorithm compared to the greedy algorithm is False statement.
It is not easier to come up with a correctness proof of the divide and conquer algorithm compared to the greedy algorithm. The correctness proof of a divide and conquer algorithm is more difficult than a greedy algorithm since it involves breaking down an algorithm into multiple sub-problems and then proving the correctness of the algorithm with respect to each sub-problem. On the other hand, the correctness proof of a greedy algorithm is relatively simple and involves determining if a given solution is optimal. Additionally, the correctness proof of a divide and conquer algorithm requires more complex mathematical analysis such as induction, recurrence relations, or complexity analysis. This makes it more difficult to come up with the correctness proof of the divide and conquer algorithm than the greedy algorithm.
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4. *
This pattern of squares continues. Which equation below relates the number of squares, n, in a picture to the size number, s ?
Size 1
Size 2
a) n=s+4
b) n=4 s
c) n=4 s+1
d) s=4 n
A
B
c
D
The required equation that following the pattern is n = 4s+1. So the option c is correct.
In the given question, we have to choose which equation below relates the number of squares, n, in a picture to the size number, s.
The given options are:
a) n = s+4
b) n = 4s
c) n = 4s+1
d) s = 4n
We find the pattern we firstly observe the given diagram closely.
As we can see that in first diagram have 5 blocks.
In second diagram have 9 blocks.
In third diagram have 13 blocks.
So, if the number of squares, represent by n, in a picture and the size number, represented by s, so the required equation that following the pattern is n = 4s+1. So the option c is correct.
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Ian's car can go 165 miles on 5 gallons of gas. During a drive last weekend, Ian used 6 gallons of gas. How far did he drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ian drove last weekend instead of how much gas he used.
The distance that Ian can drive is 198 miles.
How far did Ian drive?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Here, Ian's car can go 165 miles on 5 gallons of gas. The mile per gallon will be:
= 165 / 5
= 33 miles per gallon.
Therefore, the miles in 6 gallons will be:
= 33 × 6
= 198 miles.
The distance is 198 miles.
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Which of the following is an example of a function with a domain (-∞,+) and a range (-∞,+∞)?
Answer:
Signum function
Step-by-step explanation:
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Question 7
The cone will fit in 4 times and the volume of the cone is 535.89 in³
Volume of a ConeTo solve this problem, we have to find the volume of the cone and the volume of the sphere.
The formula of volume of a cone is given as;
V = 1/3πr²h
v = volume of the coner = radius of the coneh = height of the coneWe need to calculate the volume of the sphere which is given as
V = 4/3 πr³
The volume of the ball = 4/3 * 3.14 * 8³ = 2143.57in³
The volume of the cone = 1/3 * 3.14 * 8² * 8 = 535.89 in³
The number of times it will fit into will be 2143.57 / 535.89 = 4
It will fit in 4 times
b)
The volume of the cone is 535.89in³
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the model that includes as predictors all independent variables but no quadratic or interaction terms.
When each independent variable is changed by one unit, use linear regression to get the mean change in the dependent variable. Polynomials can be used to simulate curvature as well as to add interaction effects.
An entire second order model is what?
The x1 and x2 linear terms, the x12 and x22 second-degree terms, and the x1x2 interaction term make up the entire second degree polynomial model. As could be used to represent the estimated model.
Which kind of model would you apply to discover the relationship between the dependent and independent variables?
Considering a one-unit change in each independent variable, use linear regression to determine the mean change in a dependent variable. To represent curvature and take interaction effects into account, you may also employ polynomials.
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The complete question is "Consider a regression analysis with three independent variables x1,x2, and x3. Give the equation for the following regression models: a. The model that includes as predictors all independent variables but no quadratic or interaction terms. b. The model that includes as predictors all independent variables and all quadratic terms. c. All models that include as predictors all independent variables, no quadratic terms, and exactly one interaction term. d. The model that includes as predictors all independent variables, all quadratic terms, and all interaction terms (the full quadratic model)."
Show that Sin3xCos3x is the same as Sin 6x
The solution to the trigonometric equation is sin( 6x ) = 2sin(3x)cos(3x)
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the equation be represented as A
Now , the value of A is
A = sin (6x)
From the trigonometric relations ,
The value of sin( 2x ) = 2sin(x)cos(x)
Now , when x is replaced by 6x
Substituting the values in the equation , we get
sin ( 6x ) = 2 sin ( 6x/2 ) cos ( 6x/2 )
On simplifying the equation , we get
sin ( 6x ) = 2 sin ( 3x ) cos ( 3x )
So , the value of the trigonometric relation is
sin(6x) = 2sin(3x)cos(3x)
Hence , the equation is sin(6x) = 2sin(3x)cos(3x)
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Calculate and then write the reciprocal of your answer.
2/43 of the difference of 3 2/15 and 2 5/12
The reciprocal of 2/43 of the difference between 3 2/15 and 2 5/12 is 30.
Here, we have to subtract 2 mixed fractions i.e
=> (3 2/15) - (2 5/12)
which when converted to a proper fraction is equal to,
=> (47/15) - (29/12)
= 43/60
∵ (3 2/15) - (2 5/12) = 43/60
now, 2/43 of the difference of 3 2/15 and 2 5/12,
=> (2/43) × (43/60) = 1/30............(i)
taking the reciprocal of the value obtained above,
∴ reciprocal of 1/30 = 30.
Thus, The reciprocal of 2/43 of the difference between 3 2/15 and 2 5/12 is 30.
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What is the measure of angle I? (number only)
If H is
102°
Answer:<I=78
Step-by-step explanation:
<1 and 102 are supplementary angles so they add to 180 degrees
<1 + 102 = 180
Subtract 102 from each side
<1 + 102 -102 = 180-102
<1 = 78
Generaly speaking, the amount of gun powder particles found around a bullet hole is ____ to the distance from which the weapon was fired:
The amount of gun powder particles found around a bullet hole is directly related to the distance from which the weapon was fired.
Which two forces are acting on a bullet?
Two major forces are acting on the bullet ,the forward force of the gunshot and the downward force of gravity. The first force is called aerodynamics and the other force is called gravitational.
What does the distribution of gun powder residue around the bullet hole help to determine?
The residue exit the muzzle in a cone shaped and can land on the target objects. The size and density of the residue on the object can vary with distance allowing the fire man examiner to determine proximity of shooter to the target killing when gun is fired.
Therefore, the amount of gun powder particles found around a bullet is directly related to the distance when gun was fired.
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